Write the given linear system in matrix form. Assume X = X' = X 3 5 1 dx dt dy dt dz dt = −3x + 4y + e¯t sin(2t) = 5x + 9z+ 4e¯t cos(2t) = y + 8z - e-t 4 9 8 1 4 -1 X + (:))

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A: Given linear system X'=25-13X+1-1et

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Q: Write the given linear system without the use of matrices. Assume X = dx dt dy dt dz dt || = = X' =…

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Q: Apply systematic elimination to solve the given system dx/dt = 2x + y + t -2 dy/dt = 3x + 4y - 4t

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Q: Find a (rcal) fundamental matrix for the system x' = Ax given the following A matrices. Sketch the…

A: a) A=-1-28-1 The eigen values are given by, -1-λ-28-1-λ=0⇒(λ+1)2+16=0⇒(λ+1)=±4i⇒λ=-1±4i for λ1=-1+4i…

Q: dx 4x +2y+e* +2t dt 17. Write the system in matrix form: dy -x +3y-et dt 4 2) X + -1 3) 4 2) X+e +2t…

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Q: Why can we not write the following predator prey model in matrix form X'(t) = AÑ(t)? x'(t) = ax(t) —…

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Q: 2. Find the values of x, y and z from the system of equations: by using matrix tan²=-=-1 x²+3=7 -y²…

A: 2. Find the values of x, y and z from the system of equations, by using matrix.,,

Q: Give the General Solution.  (d/dt)(vector(x)) = matrix(2,3,-3,2)vector(x)

A: Given that,  ddtx1x2=23-32x1x2 The corresponding linear equations are, x1'=2x1+3x2x2'=-3x1+2x2…

Q: 3. dx dt dy (b) -=5x-y+z -=-x+9y-3z dt dz =-2x+2y + 4z dt (a) For the system above, define matrix A…

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Q: dx = 4x +2y+e'+t dr Write the system in matrix form: dy - 2x - y+ 3e' di 4 A. X'= 1 4 B.X' = 2 -1 3…

A: We have to find the system in matrix form.

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Q: Write the given system in the matrix form x' = Ax + f. dx -=t³x-y-z+t . = etz - 2 =tx-y+9z-e¹ dy dt…

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Q: Let Enter your answers in terms of the variable t. 2e³t 8e-t -4e³t+2€¯ -6e³t+ 5e-t 3e³t 20e-t Show…

A: It is given that: P=9-415-7, x1→t=2e3t-8e-t3e3t-20e-t and x2→t=-4e3t+2e-t-6e3t+5e-t

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Q: -dx₁ (t) dt dx₂ (t) dt 3x₁ (t) + x₂(t)- 2x3(t) — = -x₁ (t) + 2x₂(t) + 2x3 (

A: Given system can be written as  x1'x2'x3'=31-2-122001x1x2x3+-102ut

Q: Consider the following nonhomogeneous linear system: Y = Y2 + e* Y2 = Y1 – 3e3t - 2.Using MUC, which…

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Q: Consider the system, & use Computer algebra systems to solve systems         dx/dt = 4x - 3y,…

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Q: Write the given system in the form x' = P(t)x+f(t) x' = y+z, y' = z+x, z' = 5y-7

A: Given system is x' = y + zy' = z + xz' =5y -7z Take x, y, z are dependent variables and depend on t…

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A: The given system is as follows. ddtX=-210-2X Find the eigenvalues of the coefficient matrix as…

Q: For a linear system in 2 dimensions, dx dt = x(t) Ax, where x = y(t) and A is a 2 × 2 constant…

A: 1) Proof:   2) Eigen values and eigen vectorsStep 3: Step 4:

Q: X' = Write the given linear system in matrix form. Assume X = dx dt dy dt X' = DETAILS dz dt = x - y…

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Q: Find the general solution of the system x'(t) = Ax(t) for the given matrix A. 1 4 A = x(t) =

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